Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#500168 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #24033 |
| commutator, Frattini, cosocle | C22×C8 | C26 |
| prime radical | C22×#61079 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C22×#2932 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
69144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213937 |
| maximal normal subgroup of | C22×#72213937 |
Past the SmallGroups library coverage — no SmallGroups id.